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ED 355 356 



CE 063 171 



AUTHOR 
TITLE 



INSTITUTION 
SPONS AGENCY 



PUB DATE 
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PUB TYPE 



Rasmus sen 9 Bonnie 

Pre-SPC Math for Foundry Workers. A Lesson Developed 
for Robinson Foundry and Bodine-Robinson as Part of a 
National Workplace Literacy Program. 
Central Alabama Community Coll., Alexander City. 
Office of Vocational and Adult Education (ED), 
Washington, DC. National Workplace Literacy 
Program. 
Mar 93 

81p.; For related workplace literacy basic skills 
documents, see ED 352 463-464. 
Guides - Classroom Use - Teaching Guides (For 
Teacher) (052) — Tests/Evaluation Instruments (160) 



EDRS PRICE 
DESCRIPTORS 



IDENTIFIERS 



MF01/PC04 Plus Postage. 

Addition; Adult Basic Education; Arithmetic; Decimal 
Fractions ; ^'Foundries ; ^Individual ized Instruction; 
Instructional Materials; Integrated Curriculum; 
^'^Mathematics Instruction; Metal Industry; Metal 
Working; ""^Pacing; '^Quality Control; Standards; 
Subtraction; Units of Study 

National Workplace Literacy Program; ^Statistical 
Process Control; ^Workplace Literacy 



ABSTRACT 

Developed as part of a National Workplace Literacy 
Program, this lesson focuses on terms and mathematical operations 
associated with Statistical Process Control (SPC) in the foundry 
industry. With appropriate assistance and preparatory work, workers 
testing between grades 4 and 9 on the Test of Adult Basic Education 
Locator should be able to use the lesson. The individualized lesson 
is intended to supplement small-group SPC activities. It teaches 
terms and mathematics used in quality control at Bodine-Robinson and 
Robinson Foundry. Reading material is followed by questions that ask 
about the instructional material. Some terms that are covered include 
key characteristic, specification, aim, and control limits. 
Mathematics areas include adding and subtracting SPC measurements, 
adding and subtracting decimals, figuring averages, and figuring 
ranges. A true-false quiz on the material is provided. (YLB) 



Reproductions supplied by EDRS rre the best that can be made * 
* from the original document. * 

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PRE-SPC MATH FOR FOUNDRY WORKERS 



A Lesson Developed for Robinson Foundry and Bodine-Robinson as 
part of a National Workplace Literacy Program 

March, 1993 



This lesson was developed during a National Workplace 
Literacy Project to augment small group teaching. The 
lesson teaches math and reading skills needed by workers 
in the metalcasting industry. Skills and understandings 
focused on include these: adding, subtracting and dividing 
decimal numbers; figuring averages and ranges; 
understanding percentages; reading chemistry symbols; 
using SPC terminology; using metalcasting terminology; and 
using information presented in table form. 
The learning package is structured to be used by 
individual learners. They read, study charts, answer 
questions about the information, and check whether their 
answers are correct. Responses for both correct and 
incorrect answers reinforce learning. A pre- and post-test 
is included. 



Bonnie Rasmussen 

Curriculum Development Specialist 



INTRODUCTION 



PO Box 1235 

Alexander City, AL 35010 
205 329 8481 



ERIC 



2 BEST COPY fiEILSBlE 



In this lesson on 

Pre-SPC MATH 

you will learn about the terms and math used in Quality Control 
at Bodine-Robinson and Robinson Foundry. 

As you read through the lesson, you will be asked questions about 
what you are learning. 

Finally, you will do a short quiz on the lesson. 



ERLC 



1 



SPC charts keep track of key characteristics in the manufacturing 
process. For instance, charts keep track of these things: 



amount of zinc in the holding furnace when pouring Ford Manifolds 
amount of moisture content in sand from suppliers 
amount of silicon in a test button from CL 30a iron 



A wrong amount of any key characteristic gives you a defect. For 
example, too much silicon in CL 30a makes brittle iron. 



The right amount for each key characteristic is figured out by 
the lab. 

Here are two specifications the lab has set for new sand in the 
Bodine-Robinson process . 



B-R NEW SAND 

key characteristic specification 

moisture content . 1% maximum 

loss on ignition .22% maximum 



moisture content: amount of water in the sand 

loss on ignition: amount of material in the sand mixture that 

is not sand (for instance, sticks that 
ignite, or burn up, during testing) 



3 

BEST COPY AVAILABLE 

ERIC 



The lab's specification often sets a maximum for a key 
characteristic. You can't have more than •!% of moisture in new 
sand, for instance. 



B-R New Sand 

key characteristic specification 

% moisture content .1 maximum 



BEST COPY AVAILABLE 



other times, the specification will be an exact number, or 

aim point. You should try to get exactly 3.25% carbon in CL 30a 

iron. 3.25% is the aim. 



key characteristic 



% carbon (CL 25 iron) 

% carbon (CL 20 iron) 

% carbon (CL 30a iron) 

% carbon (CL 35 iron) 



R-F CL 30a iron 

Specification 

Aim 

3.49 
3.90 
3.25 
3.15 



BEST COPY AVAILABLE 



since you can't hit the aim point exactly every time, upper 
control limits (UCL) and lower control limits (LCL) are also set 
by the lab. In other words, CL 30a iron is OK if you get between 
3*20% and 3.30% of carbon. (You might notice that the aim point, 
3.25%, is right in the middle of the UCL and LCL.) 



RF CL 30a iron 



Xey characteristic 



Specification 



Aim 



Control Limits 



% carbon (CL 25 iron) 

% carbon (CL 20 iron) 

% carbon (CL 30a iron) 

% carbon (CL 35 iron) 



3.49 
3.90 
3.25 
3.15 



3.44 
3.80 
3.20 
3.00 



3.54 
4.80 
3.30 
3.10 



SESf COPY mum 



Let's look at the aim and control limits of CL 30a iron to see 
what they mean. The measurements have to do with the amount of 
carbon and other ingredients in the mix. 



key characteristic Specification 

Aim Control Limits 

% carbon (CL 30a iron) 3.25 3.20-3.30 



The aim point is 3.25% The best amount of carbon in CL 30a 
iron is 3.25% 



BEST COPY AVAILABLE 



In the square below, 3,25% is darkened. 























































































































































































ii 





















The square has been divided into 100 equal small squares. Three 
small squares along with a fourth of another square is equal to 
3.25% That portion of the iron mix should be carbon. 



Obviously, very small amounts of carbon make a big difference. 



8 



In the square below, 10.00% is darkened. 























■ 






■ 


■ 












■ 






■ 


■ 












■ 






■ 


■ 












■ 






■ 


■ 












■ 






■ 


■ 












■ 






■ 


■ 












■ 


■ 




i 


■ 












■ 


■ 


■ 


■ 


■ 












■ 


■ 


E 


■ 


■ 



The square has been divided into 100 equal small squares. 10 of 
the small squares is equal to 10.00% 



9 



In the square below, what percentage is darkened? 





















































































































































































a 























Of the 100 equal small squares, 1 1/2 squares or 1.5% has been 
darkened. 



10 



ERIC 



12 



Most of the key characteristic specifications are for very small 
amounts. Here are the aim point percentages, in color, for CL 
30a iron: 



Aim color 

% carbon 3.25 bUie 

% silicon 2.15 yellow 

% manganese .55 pink 

% chromium .08 green 



% carbon 



Aim 

3.25 



If the Quick Lab shows that the amount of carbon is 2.25%, you 
need to know how far off you are from the aim point. 

Subtract like this: 3.25 

- 2.25 
1.00 



ERIC 



Jc;^^ COPY AVAILABLE 

14 



You can add and subtra^-t SPC measurements, as long as you line up 
the decimal points, like this: 

3.5 6.4 
+ 3^ - 3^ 

6.6 3.4 



13 



JL O 



What is the answer to these problems? 



3.5 
+ 3.5 



6.4 

- .5 



Add the two fives, 
carry the one, and 
add 3+3+1 to get 7.0 



3.5 
+ 3.5 
7 . 0 



Borrow one from the six, 
subtract 5 from 14 to get 
9. Then subtract 0 from 
5 to get 5 . 

6.4 
- .5 
5.9 



14 



ERIC 



You need to be able to add and subtract decimals to use SPC 
control charts. 

The next few pages will review SPC words we've been using, and 
give you practice in adding and subtracting decimal numbers. 

Use the answer sheet for writing down your answers. DO NOT WRITE 
IN THIS BOOK. 



15 



± i 



What fits best in the blank below? 

aO (UCL) Upper Control Limit 
b*) key element 
c/) random sample 



A wrong amount of any gives you a defect. For 

instance, too much silicon in CL 30a makes brittle iron. 



Turn the page for the correct answer. 



a* This is not the right answer. 

The Upper Control Limit (UCL) shows how high a measurement can be 
and still be OK. For instance, the UCL for carbon in CL 30a iron 
is 3.30 



b. This is the correct answer. 

A wrong amount of any key element gives you a defect. For 
instance, too much silicon in CL 30a makes brittle iron. 



c. This is not the best answer. 

A random sample is taken and put on the control chart. But the 
sample is of a key element, such as silicon, carbon, and other 
elements. 



17 



What fits best in the blank below? 

a*) (UCL) Upper Control Limit 
bO key element 
c.) random sample 



SPC charts keep track of each 
manufacturing process • 



Turn the page for the correct answer. 



18 



a. This is not the right answer. 

The Upper Control Limit (UCL) shows how high a measurement can be 
and still be OK. For instance, the UCL for carbon in CL 30a iron 
is 3.30 



b* This is the correct answer. 

SPC charts keep track of each key element in the manufacturing 
process . 

c. This is not the best answer. 

An aim point is the measurement you want to achieve. But what 
you are measuring is the amount of a key element. 



19 



21 



What fits best in the blank below? 



a,) specification 
h.) estimation 
c.) sample 



The lab's often sets a maximum for a key 

characteristic. You can't have more than •!% of moisture in new 
sand, for instance. 



Turn the page for the correct answer. 



ERLC 



20 

22 



a. This is the correct answer. 



The lab's specification often ssts a maximum for a key 
characteristic. You can't have more than .1% of moisture in new 
sand, for instance. 

b. This is not the right answer. 

An estimation is a guess or an approximation. A specification, 
on the other hand, is the number set by the lab as the goal. 

c. This is not the right answer. 

A sample is a part of the work that is measured and put on the 
control chart. But the specification is the number set by the 
lab as the goal. 



Which of the following words fits best in the blank below? 

a . ) specification 

b. ) estimation 

c. ) sample 

Other times, the will be an exact number, or 

aim point. You should try to get exactly 3.25% carbon in CL 30a 
iron. 



Turn the page for the correct answer. 



a. This is the correct answer. 



Other times, the specification will be an exact number, or aim 
point. You should try to get exactly 3.25% carbon in CL 30a 
iron. 



h. This is not the right answer. 

An estimation is a guess or an approximation. A specification, 
on the other hand, is the number set by the lab. 



c. This is not the right answer. 

A sample is a part of the work that is measured ana put on the 
control chart. But the specification is the number set by the 
lab as the goal. 



what fits best in the blank below? 



a. ) control chart 

b. ) key element 

c. ) random sample 



The right amount for each 
lab. 



is figured out by the 



Turn the page for the correct answer < 



24 



ERLC 



a. This is not the best answer • 

A control chart is a graph which shows you how well your job is 
running. 



b. This is the correct answer. 

The right amount for each key element is figured out by the lab. 

c. This is not the best answer. 

A random sample is taken and put on the control chart. But the 
sample is of a key element, such as silicon, carbon, and other 
elements . 



ERLC 



25 



What fits best in the blank below? 

a. ) statistical process co trol (SPC) and non-statistical 

process control (N-SPC) 

b. ) lost foam process (EPS) and Evaporative Polystyrene System 

(EPS) 

c. ) upper control limits (UCL) and lower control limits (LCL) 



You might notice that the aim point, 3.25%, is right in the 
middle of the and 



Turn the page for the correct answer. 



a. This is not the right answer • 



Statistical process control (SPC) is a way of using number facts 
to keep track of quality. 

The upper and lower control limits, on the other hand, are found 
on SPC charts. If sample measurements fall within the upper and 
lower control limits, things are going OK. 



b. This is not the right answer. 

The lost foam process is another name for the Evaporative 
Polystyrene System, or EPS. 

The upper and lower control limits, on the other hand, are found 
on SPC charts. If sample measurements fall within the upper and 
lower control limits, things are going OK. 



c. This is the correct answer. 

You might notice that the aim point, 3.25%, is right in the 
middle of the upper control limits UCL) and lower control limits 
(LCD . 



What percentage of the large square is darkened? 



a. 50 of the hundred small squares, or 50% 

b. 3 of the hundred small squares, or 3.0% 

c. 1 and-a-half of the hundred small squares, or 1.5% 



Turn the page for the correct answer. 



ERIC 



m\ mn available 

28 



a. This is the correct answer. 

Fifty of the hundred small squares, or 50% are darkened. 

b. This is not the right answer. 

Count the squares to get the right aiiswer: 50/100 

c. This is not the right answer. 

Count the squares to get the right answer: 50/100 



What percentage of the large square is darkened? 



a. Fifty of the hundred small squares, or 50% 

b. Three of the hundred small squares, or 3.0% 

c. One and-a-half of the hundred small squares, or 1.5% 

















J' .* * ft 























































































































































































Turn the page for the correct answer. 



30 



ERIC 



a. This is not the right answer. 

Count the squares to get the right answer: 3/100 

b. This is the correct answer. 

Three of the hundred small squares, or 3.0% are darkened. 

c. This is not the right answer. 

Count the squares to gei: the right answer: 3/100 



31 



What percentage of the large square is darkened? 



a. Fifty of the hundred small squares, or 50% 

b. Three of the hundred small squares, or 3,0% 

c. One and-a-half of the hundred small squares, or 1,5% 



Turn the page for the correct answer. 



ERIC 



32 



a. This is not the right answer. 

Count the squares to get the right a*-swer: 1 1/2/100 

b. This is not the right answer. 

Count the squares to get the right answer: 1 1/2/100 

c. This is the correct answer. 

One-and-a-half of the hundred small squares, or 1.50% are 
darkened . 



33 



4^ 



What percentage of the large square is darkened? 



a. ) Ten of the hundred small squares, or 10% 

b. ) Three of the hundred small squares, or 3.0% 

c. ) One-and-a-half of the hundred small squares, or 1.5% 































































































































































































1 
1 











Turn the page for the correct answer. 



34 



ERIC 



a. This is the correct answer. 

Ten of the hundred small squares, or 10% are darkened. 

This is not the right answer. 
Count the squares to get the right answer: 10/100 

c. This is not the right answer. 

Count the squares to get the right answer: 10/100 



ERLC 



35 



O 4 



What is the correct answer? 



1.25% 
+ 1.01% 



a. ) 2.80% 

b. ) 2.26% 
C.) 22.6% 



Turn the page for the correct answer. 



ERIC 



36 



a. This is not the right answer. 



b. This is the correct answer. 

1.25% 
+1.01% 
2.26% 



o. This is not the right answer. 



37 



ERIC 



9^ G;} 



What is the correct answer? 



1.90 
+ 1.20 



a. ) 2.11 

b. ) 3.11 

c. ) 3.10 



Turn the page for the correct answer. 



ERIC 



38 

40 



a. This is not the right answer. 



b. This is the correct answer. 

1.90 
+ 1.20 
3.11 



c. This is not the right answer. 



39 



What is the correct answer? 



3.25 
- 3.00 



a. ) .25 

b. ) 6.25 

c. ) 25.00 



Turn the page for the correct answer. 



ERIC 



40 



This is the correct answer. 



3.25 
3.00 
.25 



This is not the right answer. 



This is not the right answer. 



What is the correct answer? 



3 .50 
- 2.19 



a. ) 1.31 

b. ) 1.41 

c. ) 0.131 



Turn the page for the correct answer. 



ERIC 



42 



-^4 



This is the correct answer. 



3.50 
2.19 
1.31 



This is not the right answer 



This is not the right answer 



You have finished the review questions on terms and math for the 
first part of the lesson. Now you'll learn about more terms and 
math used in Quality Control at Bodine-Robinson and Robinson 
Foundry . 

Each time an SPC measurement is taken for a Key Characteristic, 
you get some idea of how close you are to the lab's 
specif ication* If you write down several of the measurements, you 
can average them. 



ERIC 



44 



- HO 



Here's how you figure an average: 

The amount of silicon measures at 7.09, then at 7.04, and finally 
at 6.93. 



Add up the measurements: 7.19 

7.24 
+ 6.93 
21.36 

Divide by 3, since there 
are three measurements 7 . 12 

you added together : 3/21.36 

21 
0 3 



3 

06 
_6 
0 

The average amount of silicon that shift was 7.12 



45 



ERIC 



An average, then, evens out the high and low measurements, like 
this: 



Two are six feet tall, 
two are five feet tall. 



6 






6 
H 








3 








I 








"7 









All four are now five-and-a-half feet tall. 



5 








3 








l 
/ 









46 

ERIC 



Here's another example of how to figure an average. (By the way, 
the silicon itieasureitients we are averaging are those taken in the 
holding furnace when pouring Ford Manifolds. The aim point is 
7.25.) 

7.00 
7.34 
+ 7.38 
21.72 



7.24 
3/21.72 



47 



Why, in this example do we divide by 



7 .00 
7.40 
6.93 
+ 7.25 
28.58 



7.15 
4/28.58 



48 



If you have four measurements, you have to divide by four. 
(You always divide by the number of measurements.) 



The next few pages will give you practice in adding and 
subtracting decimal numbers. 

Use thfe answer sheet f.r writing down your answers. DO NOT WRITE 
IN THIS BOOK. 



49 



51 



On SPC charts you will see an X. That means average, and is 
pronounced ' X-bar ' . 



What is the correct answer? 

4 
4 

+7 
15 

5 

3/15 



a. X = 15 

b. X = 5 
C. X = 3 



Turn the page for the correct answer. 



50 




a. This is not the right answer. 

Fifteen is the sum of the sample measuremonts . 



b. This is the correct answer. 

4 
4 

±2 
15 

_5 
3/15 

Average (X) = sum of samples 

niunber of samples 



e. This is not the right answer. 

Three is the number of sample measurements. 



51 

ERIC 



What is the correct answer? 



1 

4 

+7 



3/ 



a. 


X = 


12 


b. 


X = 


5 


c. 


X = 


4 



Turn the page for the correct an. wer. 



ERIC 



52 



This is not the correct answer 



This is not the correct answer 



This is the correct answer. 



1 
4 

±z 

12 

4 

3/12 

Average (X) = sim of samples 

niimber of samples 



What is the correct answer? 

3.25 
3.23 





/ 






a. 


X = 


3 


.24 


b. 


X = 


4 


.24 


c. 


X = 


6 


.46 



Turn the page for the correct answer. 



54 

5d 



a. This is the correct answer. 



3.25 
3.23 
6.48 

3 .24 
2/6.48 



Average (X) = sxim of samples 

number of samples 



b. This is not the correct answer 



c. This is not the correct answer 



55 



What is the correct answer? 



7.21 
7.44 
+1 .21 



I 



a. X = 21.92 

b. X = 10.96 
C. X = 7.31 



Turn the page for the correct answer. 



ERIC 



56 



58 



a. 



This is not the correct answer. 



b. This is not the correct answer. 



c. This is the correct answer. 

7.21 

7.44 
+7.27 
21.92 

7.31 
3/21.92 

Average (X) = stun of samples 

number of samples 



ERIC 



57 



Another important SPC term is ra 
the range of the second group of 
on the left? 

Problem 1: What is the 
range of the three 
measurements? 



ga, or R. Can you figure out 
numbers by studying the example 



Problem 2: What is the 
range of the three 

measurements? 



Measurements 

7,21 

7,44 

7,27 



Measurements 

7,01 

7,04 

6.93 



7.44 
-7.21 
.23 



R 



23 



R 



58 

CO 



Measurements 



Arithmetic to figure R 



7.01 
7.04 
6.93 



7.04 
- 6.93 
.11 



= .11 



Just subtract the smallest measurement from the biggest 
measurement . 



The next few pages will give you practice in figuring ranges. 

Use the answer sheet for writing down your answers. DO NOT WRITE 
IN THIS BOOK. 



59 



61 



What is R? 



7.74 






7.28 






7.20 






a. 


R = 


.46 


b. 


R = 


.54 


c. 


R = 


7.41 



Turn the page for the correct answer. 



60 

ERIC 



a. This is not the right answer. 

b. This is the correct answer. 

Correct arithmetic 
7.74 
- 7.20 

.54 = R 



Sample measureiaents 
7.74 
7.28 
7.20 



Range (R) = Largest measurement minus smallest measurement 



c. This is not the right answer. 



What is R? 



7.44 
7.46 
7.48 



a. 


R = 


.02 


b. 


R = 


.04 


c. 


R = 


.06 



Turn the page for the correct answer. 



62 




a* This is not the right answer. 



b* This is the correct answer. 

Sample measurements Correct arithmetic 
7.44 7.48 
7.46 - 7.44 
7.48 .04 = R 

Range (R) = Largest measurement minus smallest measurement 



c. This is not the right answer. 



63 



What is R? 



7.44 
7.44 
7.41 

a. R = 7.43 

b. R = .03 
C. R = 1.29 



Turn the page for the correct answer. 



ERIC 



64 



a. This is not the right answer. 



b. 



This is the correct answer. 



Sample measurements 



7 .44 
7.44 
7 .41 



Correct arithmetic 
7 .44 
- 7.41 

.03 = R 



Range (R) = Largest measurement minus smallest measurement 

c. This is not the right answer. 

You have finished the review questions on terms and math for the 
lesson. The next few pages explain further how the average (X) 
and Range (R) give useful quality control information. 



ERIC 



65 

C7 



Below, the average column on the right shows us how close we are 
to the aim point after smoothing out the highs and lows of 
individual measurements. 



Another way of looking at it is this: if the first three furnaces 
(measuring 7.01, 6.82, 7.22) could be mixed together, the whole 
big batch would measure 7.02. 

(Remember, this example is of the percentage of silicon in the 
holding furnace when pouring Ford Manifolds, and the aim point is 



Measurements 



Average (X) 



7.01, 6.82, 7.22 
7.00, 7.08, 6.93 
7.21, 7.44, 7.27 



7.02 
7.00 
7.31 



7.25.) 



What would you expect the missing numbers to be, approximately 







Measurements 


Average (X) 


7.01, 6.82, 7.22 


7.02 


7.00, 7.08, 6.93 


7 . 00 


7.21, 7.44, 7.27 


7 .31 




7.04 


, f 





67 



Did you expect one of the missing numbers to be as high as 12.05, 
or as low as 2.00? 



Measurements Average (X) Range (R) 

7.01, 6.84, 7.22 7.02 .38 
7.00, 7.08, 6.95 7.02 .13 

7.02, 2.00, 12.05 7.02 10.05 



Of course, a measurement of either 2.00 or 12.05 (for silicon in 
the holding furnace when pouring Ford manifolds) would be very 
unusual . 



ERIC 



68 



7U 



The point is, though, the average (X) smooths out the 
differences, while the range (R) shows us how far apart the 
measurements are. 



Measurements Average (X) Range (R) 

7.01, 6.84, 7.22 7.02 .38 
7.00, 7.08, 6.95 7.02 .13 

7.02, 2.00, 12.05 7.02 10.05 



69 



ERIC 



without the range, you can't predict accurately. Look at the 
ways that 3 numbers can average the same but have different 
ranges. 









Measurements 


Average (X) 


Range 


7.01, 6.84, 7.22 


7.02 


.38 


7.00, 7.08, 6.95 


7.02 


.13 


7.02, 2.00, 12.05 


7.02 


10.05 



70 



In this lesson you have learned about the terms and 
math used in SPC. 

Next you will do a short quiz. 

Use the answer sheet for writing down your answers. DO NOT WRITE 
IN THIS BOOK. 



71 



o 73 
ERIC 



Quis 



Answer true or false for each question. 

1. The lab's specification for a key element may be a maximum or 
a minimum, but never an aim point. 

a . ) true 

b. ) false 



2. The Control Limits for CL 30a iron are 3.20-3.30. That 
means that a measurement of 3.24 is within the limits. 



a . ) true 

b. ) false 

3. A large square is divided into 100 equal smaller squares. 
Three and a half small squares are equal to 3.5% of the large 
square . 

a . ) true 

b. ) false 



4. 3.25 
+ 3.25 
6.50 

a . ) true 

b. ) false 



5. 7.21 
- 7.09 
.13 



6. X on an SPC chart means the average, or mean. 

a . ) true 

b. ) false 

7. To figure an average (X), add up the items and divide by the 
number of items added. 



a . ) true 



bO false 

8. To figure a range, add the top two numbers* 

a • ) true 
b*) false 

9. This average is figured correctly. 
measurements arithmetic 
7.02, 6.82, 7.22 7. 0 27 . 02 



6.82 
+ 7.22 
21.06 



3/21.06 



a. ) 

b. ) 



true 
false 



10. 



This range is figured correctly. 



measurements 
7.01, 6.32, 



arithmetic 



7.22 



7.22 



" 6.82 
.40 



a . ) true 

b. ) false 



Turn the page for the correct answers. 



73 



75 



Answers to Quis 

Answer true or false for cuicli question* 

1. The lab's specification for a key element may be a maximum or 
a minimum, but never an aim point. 

false 

2. The Control Limits for CL 3 0a iron are 3.20--3.30. That 
means that a measurement of 3.24 is within the limits. 

true 

3. A large square is divided into 100 equal smaller squares. 
Three and a half small squares are equal to 3.5% of the large 
square. 

true . 

4. 3.25 
4- 3,25 

6.50 

true 

5. 7.21 
- 7.09 

.13 

false 

6. X on an SPC chart means the average, or mean, 
true 

7. To figure an average (X), add up the items and divide by the 
number of items added. 

true 

8. To figure a range, add the top two numbers, 
false 

9. This average is figured correctly. 

measurements arithmetic 

7.02, 6.82, 7.22 7.0 27.02 

6.82 3/21.06 



21.06 



+7.22 



true 

10. This range is figured correctly. 

measurements arithmetic 
7.01, 6.82, 7.22 7.22 

- 6.82 
.40 



true 



75 



ERIC 



ANSWER SHEET 



For each question, circle your answer, then check (on the next 
page in the lesson book) whether it is right. 

page 16 

a. ) 

b. ) 

c. ) 



Page 18 

a. ) 

b. ) 

c. ) 



Page 20 

a. ) 

b. ) 

c. ) 



Page 22 

a. ) 

b. ) 

c. ) 



page 24 

a. ) 

b. ) 

c. ) 



page 2 6 

a. ) 

b. ) 

c. ) 



Page 28 

a. ) 

b. ) 

c. ) 



1 o 



ERIC 



Page '30 

a. ) 

b. ) 

c. ) 



Page 32 

a. ) 

b. ) 

c. ) 



Page 34 

a. ) 

b. ) 

c. ) 



page 36 

a. ) 

b. ) 

c. ) 



Page 38 

a. ) 

b. ) 

c. ) 



Page 40 

a. ) 

b. ) 

c. ) 



Page 42 

a. ) 

b. ) 

c. ) 



Page SO 

a. ) 

b. ) 

c. ) 

Page 52 

a. ) 

b. ) 

c. ) 

Page 54 

a. ) 

b. ) 

c. ) 

Page 56 

a. ) 

b. ) 

c. ) 



Page 60 

a. ) 

b. ) 

c. ) 

Page 62 

a. ) 

b. ) 

c. ) 

Page 64 

a. ) 

b. ) 

c. ) 



Quiz 
1. 

a. ) true 

b. ) false 

2. 

a • ) true 
b.) false 

3. 

a . ) true 

b. ) false 

4. 

a • ) true 
b.) false 

5. 

a • ) true 
b.) false 

6. 

a. ) true 

b. ) false 

7. 

a . ) true 

b. ) false 

8. 

a • ) true 
b.) false 

9. 

a. ) true 

b. ) false 

10. 

a. ) true 

b. ) false 



81 

ERIC